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The generation of preferences represented as CP-nets for experiments and empirical testing has typically been done in an ad hoc manner that may have introduced a large statistical bias in previous experimental work. We present novel polynomial-time algorithms for generating CP-nets with n nodes and maximum in-degree c uniformly at random. We extend this result to several statistical cultures commonly used in the social choice and preference reasoning literature. A CP-net is composed of both a graph and underlying cp-statements; our algorithm is the first to provably generate both the graph structure and cp-statements, and hence the underlying preference orders themselves, uniformly at random. We have released this code as a free and open source project. We use the uniform generation algorithm to investigate the maximum and expected flipping lengths, i.e., the maximum length over all outcomes o1 and o2, of a minimal proof that o1 is preferred to o2. Using our new statistical evidence, we conjecture that, for CP-nets with binary variables and complete conditional preference tables, the expected flipping length is polynomial in the number of preference variables. This has positive implications for the usability of CP-nets as compact preference models.
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Learning Tree-Structured CP-Nets with Local Search
Conditional preference networks (CP-nets) are an intuitive and expressive representation for qualitative preferences. Such models must somehow be acquired. Psychologists argue that direct elicitation is suspect. On the other hand, learning general CP-nets from pairwise comparisons is NP-hard, and --- for some notions of learning --- this extends even to the simplest forms of CP-nets. We introduce a novel, concise encoding of binary-valued, tree-structured CP-nets that supports the first local-search-based CP-net learning algorithms. While exact learning of binary-valued, tree-structured CP-nets --- for a strict, entailment-based notion of learning --- is already in P, our algorithm is the first space-efficient learning algorithm that gracefully handles noisy (i.e., realistic) comparison sets.
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- Award ID(s):
- 1215985
- PAR ID:
- 10048704
- Date Published:
- Journal Name:
- Proceedings of the ... International Florida Artificial Intelligence Research Society Conference
- ISSN:
- 2334-0762
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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